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High-Precision RCM Motion for Ophthalmic Robotics via Hierarchical QP Control and Authority-Guided Recovery Planning

Huanyu Tian, Adriana Namour, Lingyun Zeng, Zicong Wu, Sebastien Ourselin A, Lyndon da Cruz, Christos Bergeles · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27905 · cited by 0 works (OpenAlex) · open-access PDF

Korean

일반적인 목적을 가진 조작자는 소프트웨어 RCM(Remote Center of Motion)에 의한 안구 장치를 배치할 수 있습니다. 그러나 팁 작업에 불합리한 몇 가지 도달 가능한 구성에서는 RCM 및 팁 추적 목표가 충돌하고 서보 진동합니다. 우리는이 실패를 제한 유도 작업 단일성으로 공식화합니다. RCM 프로젝트의 팁 Jacobian은 팁 Jacobian이 잘 조건을 유지하는 동안 순위를 잃습니다. 따라서 효과적인 팁 권한은 목표가 도달 할 수있는 반면에 충돌합니다. 우리는 고정밀 RCM 서보 아키텍처를 구축된 단일성 복구로 공식화합니다 : 각 명령 대상의 오류에 대해 권한 지시된 팁 Jacobian은 그것에 도달하는 잘 조건을 갖춘 무장

Machine translation (Meta M2M100); the English original follows.

Abstract

General-purpose manipulators can position ophthalmic instruments under a software Remote Centre of Motion (RCM). However, at some reachable configurations that are nonsingular for the tip task alone, the RCM and tip-tracking objectives conflict and the servo oscillates. We formalise this failure as a constraint-induced task singularity: the RCM-projected tip Jacobian loses rank while the unprojected tip Jacobian stays well conditioned. Thus, the effective tip authority collapses although the target remains reachable. We present a high-precision RCM servo architecture with built-in singularity recovery: for each commanded target, an authority-guided planner selects a well-conditioned arm configuration that reaches it and plans an RCM-consistent route, executed by a fixed hierarchical-QP controller. On a 200-scenario kinematic benchmark, the complete nominal-and-recovery protocol reaches 128/128 near-singular targets and 71/72 near-joint-limit targets (100% and 99%, respectively), with the software-RCM residual below 0.142 mm. On a physical 6-DOF arm it executes across four RCM entry points, with a worst-case kinematically reconstructed RCM residual of 178 μm and a median tip-regulation error of 32μm, within the 200μm control requirement adopted for the ophthalmic task.

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Topics: Jacobian matrix and determinant, Robotics, Kinematics, Task (project management), Residual, Computer science

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